Closed-form approximations in derivatives pricing: The Kristensen-Mele approach

TL;DR

This paper explores Kristensen and Mele's closed-form approximation method for derivatives pricing, analyzing its application to various stochastic volatility models and its numerical stability across different parameters.

Contribution

It introduces and applies Kristensen and Mele's approximation approach to multiple models, assessing its stability and accuracy in derivatives pricing.

Findings

The approximation provides accurate pricing for European options.

Numerical stability varies with model choice and parameters.

The method simplifies computation of greeks.

Abstract

Kristensen and Mele (2011) developed a new approach to obtain closed-form approximations to continuous-time derivatives pricing models. The approach uses a power series expansion of the pricing bias between an intractable model and some known auxiliary model. Since the resulting approximation formula has closed-form it is straightforward to obtain approximations of greeks. In this thesis I will introduce Kristensen and Mele's methods and apply it to a variety of stochastic volatility models of European style options as well as a model for commodity futures. The focus of this thesis is the effect of different model choices and different model parameter values on the numerical stability of Kristensen and Mele's approximation.